Maximum tensile and compressive bending stresses in a beam

  1. 1. The problem statement, all variables and given/known data

    Draw the shear force and bending moment diagrams for the beam shown in Fig. 1 below. Determine the maximum tensile and compressive bending stresses and the positions at which they occur. The beam’s cross-sectional area is shown in Fig. 2.

    http://i1225.photobucket.com/albums/ee382/jon_jon_19/q2.jpg

    2. Relevant equations

    Bending Stress = Mc/I

    Where I is inertia, c is distance from neutral axis, M is the bending moment

    3. The attempt at a solution

    I have drawn the shear and bending moment forces and worked out the moment of inertia in the T-section. But I am unsure how I work out the maximum tensile and compressive bending stresses.
    How do I apply this.

    Thanks.
     
  2. jcsd
  3. PhanthomJay

    PhanthomJay 6,215
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    On the assumption that you have correctly calculated the maximum moment and moment of inertia, max stress is My/I, where y is the distance from _____ to ______? The value of y will be differnt when calculating max tensile and max compressive stress.
     
  4. PhanthomJay

    PhanthomJay 6,215
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    The bending stresses are about the axis that is horizontal to the cross section ( the x axis), thus you need to calculate and use Ix in your bending stress equations. You must not add up Ix and Iy. Also, your math is off, please recheck your numbers.
    You must of course also calculate M correctly...otherwise, you have the right approach for determining the max stresses.
     
  5. nvn

    nvn 2,124
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    dvep: You do not need to compute Iy, because there is no bending moment about the y axis. Your Ix value currently appears incorrect. Try again. Yes, M is the maximum moment in the bending moment diagram.
     
  6. nvn

    nvn 2,124
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    dvep: Your Ix value appears incorrect. Try again. Regarding the units of M, I recommend converting all units to N, mm, and MPa. Using N and mm, stresses will be N/mm^2, which is called and written MPa. Also, the bending stress formula is sigma = -M*y/Ix.
     
  7. nvn

    nvn 2,124
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    dvep: Nice work. You forgot to use y = 22 mm, and y = -38 mm. Try that again. Tensile stress is positive.

    By the way, for long numbers having five or more digits, the international standard says you can write the digits in groups of three, separated by spaces. E.g., -15 000 000 N*mm, instead of -15000000 N*mm. See the international standard for writing units (ISO 31-0).
     
  8. nvn

    nvn 2,124
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    No, you forgot the negative sign in the bending stress formula, this time. Try again. Also, typically use asterisk for the multiplication symbol, instead of "x," because "x" can easily be confused with the variable x.
     
  9. nvn

    nvn 2,124
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    dvep: Switch the words tensile and compressive, because tensile stress is positive. Also, in post 9, your units on M should be N*mm, not N*mm^2. Also, see the last paragraph of post 3087641, regarding rounding your final answer.
     
    Last edited: Jan 22, 2011

  10. Thank you nvn, you were very helpful.
     
  11. nvn

    nvn 2,124
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    dvep: By the way, it is not allowed to delete your posts, the way you did, above. They call this abuse of the Edit feature. We will hopefully let it slide this time, since you are doing such excellent work. But I just wanted to warn you, so you can stay out of trouble, next time.

    You did excellent work on your homework.
     
  12. Oh, sorry I didn't know, I won't do it again.

    Thank you again for you help.
     
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